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Pertanyaan

Hitung a , b , dan c , jika x → 1 lim ​ x 3 − 3 x + 2 a x 2 + b x + c ​ = 4

Hitung , jika

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai .

nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank dan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style.

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Pembahasan

Dengan menggunakan konsep limit, diperoleh: Jadi, nilai .

Dengan menggunakan konsep limit, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator x cubed minus 3 x plus 2 end fraction end cell equals 4 row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses end fraction end cell equals 4 row cell Untuk space straight x end cell equals cell 1 comma space bentuk space 0 over 0 space maka colon end cell row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell equals cell 4 space rightwards arrow limit as x rightwards arrow 1 of fraction numerator open parentheses x minus 1 close parentheses open parentheses x plus d close parentheses over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis end fraction equals 4 end cell row blank blank blank row cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x plus d right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end cell equals cell 4 space rightwards arrow 1 plus d equals negative 4 space rightwards arrow d equals negative 3 comma space sehingga end cell row blank blank blank row cell a x squared plus b x plus c end cell equals cell open parentheses x minus 1 close parentheses left parenthesis x minus 3 right parenthesis end cell row blank blank blank row cell a x squared plus b x plus c end cell equals cell x squared minus 4 x plus 3 end cell row blank blank cell a equals 1 comma space b equals negative 4 space dan space c equals 3 end cell end table end style 


Jadi, nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank dan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table end style.

31

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